Do the Conduction and Valence Bands of Conductors Always Overlap or Are There Exceptions?

The conduction and valence bands are key concepts in understanding the electronic properties of materials, particularly metals and semiconductors. In this exploration, we will delve into whether the conduction and valence bands of conductors always overlap or if there are any conductors with a lesser energy gap between these bands.

Understanding the Bands in Metals

Metals are unique in that they possess at least one band that is partially filled. For metals, this partially filled band is both the conduction and valence band. This means that the electrons in these bands are free to move and conduct electricity, giving metals their metallic properties. In these materials, the energy gap between the valence and conduction bands is effectively zero, allowing for a continuous range of electronic states that electrons can occupy.

The Case of Non-Metal Conductors and Semimetals

For non-metals, the situation is different. Non-metals typically have full bands in the valence region and empty bands in the conduction region, separated by an energy gap. However, there are some materials where the conduction and valence bands overlap, but at a different position in k-space, which is the momentum space divided by ?.

These materials are often referred to as semimetals, sometimes also called metalloids. Semimetals are special because they have a small overlap between the conduction and valence bands, leading to a low carrier concentration. This overlap can be significant enough to allow for some conductivity, but it is not as pronounced as in metals. Semimetals can be considered to have a "negative indirect gap," although this is a somewhat simplifying term, as the bands do not actually overlap in the traditional sense.

Exceptional Cases: Semimetals and Narrow Band Gap Semiconductors

For semimetals, there are exceptional cases where the conduction and valence bands intersect at a single point in the reciprocal space, which is often referred to as the Brillouin zone. This is a unique property that can lead to unusual electronic and magnetic behaviors. Examples of semimetals include certain transition metals and some doped semiconductors.

There is one notable exception to the above discussion: very narrow band gap semiconductors, like tin (Sn). When pure and at helium temperatures, tin behaves like a semiconductor, where electrons must cross an energy gap to move from the valence band to the conduction band. However, at room temperature, the material behaves as a conductor due to the small band gap, which allows for significant carrier concentration.

Conclusion: The Overlap Myth and Other Band Properties

While the conduction and valence bands of conductors and semimetals do show a form of overlap, this overlap is not unconditional. Semimetals and very narrow band gap semiconductors, like tin, are notable exceptions. For these materials, the concept of a zero-energy gap or a smaller gap is important, as it can affect their electrical properties significantly.

Understanding the distinctions between metals, semimetals, and narrow band gap semiconductors is crucial for designing new materials with specific electronic properties. Whether the conduction and valence bands overlap or not, the energy gap between them can have a profound impact on a material's behavior and its potential applications in electronics and other fields.